On May 27, 3:00 am, Stephen Bloch <sbl... at adelphi.edu> wrote:
> On May 26, 2009, at 3:43 PM, wooks wrote:
>> The problem with that is that English (like most natural human
> languages) is notoriously unclear and ambiguous, and mathematicians
> don't like things being unclear or ambiguous. So they invent
> specialized symbols and terms that mean EXACTLY what they're defined
> to mean, no more and no less -- not in order to be unclear, but in
> order to be clear. It IS possible to write clear, precise
> mathematics in the vernacular, without specialized symbols and terms
> -- it was done for thousands of years -- but that style tends to be
> so verbose that you forget what you were trying to prove by the time
> you get to the end of it.
>
Cohen expresses another view. This is from the preface of the 2nd
Edition of his book.
"Undergraduate Computer Science majors generally do not speak the
language of mathematical symbolism fluently, nor is it important at
their level that they do no more than try. The value of mathematical
iconography is that it enables professionals to perform their research
and communicate their results more efficiently. The symbolism is not a
profound discovery in and of itself. It is at best a means, not an
end. To those whom it is opaque, it is a hindrance to understanding.
When this happens it is mathematically dysfunctional and a pedagogical
anathema."
In the first edition he mentions that a consequence of the
mathematical rigour and sophistication of texts on Theory of
Computation is that the subjects are relegated almost exclusively to
the very advanced student.
He claims his book has no presumed background of any kind and every
mathematical concept is introduced from scratch.
A claim backed up by my personal experience and by the reviews.
http://www.amazon.com/Introduction-Computer-Theory-Daniel-Cohen/product-reviews/0471137723/ref=dp_top_cm_cr_acr_txt?ie=UTF8&showViewpoints=1